As the title says, archers will shoot at cavalry (both melee and ranged) from distance of roughly 40 metres, if you order them to charge from further distance, thay will move towards the cavalry until they reach this aforementioned distance of 40 metres and only then will they start shooting. This behaviour also aplies towards player character if it is mounted. Strangely if you dismount or if you order your mounted units to dismount archers will react from correct range. Also if you and your troops mount your horse again the archers will keep reacting from the correct distance! Even if you dismount and then remount your cav at the beginning of the battle before you are in the range of archers will the archers react correctly. I believe this bug was present for quite some time.